TY - JOUR
T1 - Nonlinear Rank-One Modification of the Symmetric Eigenvalue Problem
JO - Journal of Computational Mathematics
VL - 2
SP - 218
EP - 234
PY - 2010
DA - 2010/04
SN - 28
DO - http://doi.org/10.4208/jcm.2009.10-m1002
UR - https://global-sci.org/intro/article_detail/jcm/8516.html
KW - Nonlinear eigenvalue problem, Rank-one modification, Rank-one damping,
Low-rank damping, Picard, Successive linear approximation method, Nonlinear Rayleigh
quotient iteration, Safeguard, Global convergence.
AB - <p style="text-align: justify;">Nonlinear rank-one modification of the symmetric eigenvalue problem arises from eigenvibrations of mechanical structures with elastically attached loads and calculation of the propagation modes in optical fiber. In this paper, we first study the existence and uniqueness of eigenvalues, and then investigate three numerical algorithms, namely Picard iteration, nonlinear Rayleigh quotient iteration and successive linear approximation method (SLAM). The global convergence of the SLAM is proven under some mild assumptions. Numerical examples illustrate that the SLAM is the most robust method.</p>